Assuming your oil level is good and the crankshaft isn't frozen, it has to be something spun up by the serpentine belt. Remove the belt and spin things by hand. The things with pulleys include the AC compressor, alternator, power steering pump, idler pulley, tensioner pulley, and water pump.
That assumes the AAA guy is a competent diagnostician. He may be wrong, and you have a bad starter, wiring connection, starter relay or ignition switch.
By the way, my understanding is that AAA will cancel you if you have more than 4 call-outs in a year. Any reason you didn't just get a new battery or a jump-start box of your own after the first incident? If your battery is good and you keep running it down, how is that happening? If the reason for the run-down is a mystery, you may have a parasitic current drain and that's a problem that needs to be troubleshot.